Finite Group DatabasebetaFinite Group Databasebeta| order | 19844 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D41×D121 |
| unambiguous semidirect product | (C41×D121)⋊C2 |
| unambiguous semidirect product | (D41×C121)⋊C2 |
| unambiguous semidirect product | D4961⋊C2 |
| Fitting, derived, Hall | C41×C121 ⋊ C22 |
| Sylow | C121 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C41×C121 | C22 |
| Frattini | C11 | D11×D41 |
| socle | C11×C41 | C2×D11 |
| LCS | G ▷ C41×C121 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4961 |
1364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19844, 8);